Precession wrt invariable plane

Is it true that when a body's position is expressed as longitude and
latitude in the invariable plane system, and then recalculated for a
different epoch (assuming no proper motion), the latitude remains
unchanged?

There's some intuitive sense in the idea, but it seems to me that the
conversion from standard (J2000 or apparent) ecliptic coordinates to
invariable-plane coordinates would have to be a little more complex
than what I have seen in textbooks - or else the inclination of the
inv.p. wrt the ecliptic is more complex.

Is there a place online where this is discussed? I have seen
tantalizing references, but no link to a substantive discussion.

Axel Harvey wrote:

Is it true that when a body's position is expressed as longitude and
latitude in the invariable plane system, and then recalculated for a
different epoch (assuming no proper motion), the latitude remains
unchanged?

There's some intuitive sense in the idea, but it seems to me that the
conversion from standard (J2000 or apparent) ecliptic coordinates to
invariable-plane coordinates would have to be a little more complex
than what I have seen in textbooks - or else the inclination of the
inv.p. wrt the ecliptic is more complex.

Is there a place online where this is discussed? I have seen
tantalizing references, but no link to a substantive discussion.

I take it that you're measuring longitude in the "invariable plane
system" from the ascending node of the invariable plane on the Earth's
mean equator of date? This would be akin to the vernal equinox, but
with the I.P. replacing the ecliptic. If so, then YES -- in the
absence of proper motion, a star's latitude in the I.P. system would
stay constant.

The inclination of the I.P. wrt the ecliptic (or vice versa! depending
on how you approach the problem) is indeed rather complicated. The
ecliptic changes its orientation due to perturbations from the other
planets, most notably Venus and Jupiter. The north ecliptic pole
traces out a sequence of loops which as an ensemble do seem to be
centered on the I.P. pole (the angular momentum vector of the solar
system), but any one loop is not so centered. These are long-period
effects, and the standard third-degree polynomials for precession do
not capture them.

Precession using the invariable plane happens to have been the subject
of my Ph.D. dissertation. My advisor, Heinz Eichhorn, came up with the
idea and thought it was wonderful, and left it to me to work out the
details. I did manage to publish a 4-page article in the proceedings
of IAU Colloquium 127, but to the best of my knowledge nothing ever
came of it. A pity in some ways, as the formulations are somewhat
easier computationally with one plane being held constant.

-- Bill Owen,